%0 Journal Article %1 Brini2010417 %A Brini, Andrea %A Griguolo, Luca %A Seminara, Domenico %A Tanzini, Alessandro %D 2010 %J Journal of Geometry and Physics %K chern-simons lens space theory %N 3 %P 417 - 429 %R http://dx.doi.org/10.1016/j.geomphys.2009.11.006 %T Chern–Simons theory on lens spaces and Gopakumar–Vafa duality %U http://www.sciencedirect.com/science/article/pii/S0393044009001892 %V 60 %X We consider aspects of Chern–Simons theory on L ( p , q ) lens spaces and its relation with matrix models and topological string theory on Calabi–Yau threefolds, searching for possible new large N dualities via geometric transition for non- S U ( 2 ) cyclic quotients of the conifold. To this aim we find, on one hand, a useful matrix integral representation of the S U ( N ) C S partition function in a generic flat background for the whole L ( p , q ) family and provide a solution for its large N dynamics; on the other hand, we perform in full detail the construction of a family of would-be dual closed string backgrounds through conifold geometric transition from T ∗ L ( p , q ) . We can then explicitly prove the claim in 5 that Gopakumar–Vafa duality in a fixed vacuum fails in the case q > 1 , and briefly discuss how it could be restored in a non-perturbative setting.

@article{Brini2010417, abstract = {We consider aspects of Chern–Simons theory on L ( p , q ) lens spaces and its relation with matrix models and topological string theory on Calabi–Yau threefolds, searching for possible new large N dualities via geometric transition for non- S U ( 2 ) cyclic quotients of the conifold. To this aim we find, on one hand, a useful matrix integral representation of the S U ( N ) C S partition function in a generic flat background for the whole L ( p , q ) family and provide a solution for its large N dynamics; on the other hand, we perform in full detail the construction of a family of would-be dual closed string backgrounds through conifold geometric transition from T ∗ L ( p , q ) . We can then explicitly prove the claim in [5] that Gopakumar–Vafa duality in a fixed vacuum fails in the case q > 1 , and briefly discuss how it could be restored in a non-perturbative setting. }, added-at = {2016-08-17T12:44:33.000+0200}, author = {Brini, Andrea and Griguolo, Luca and Seminara, Domenico and Tanzini, Alessandro}, biburl = {https://www.bibsonomy.org/bibtex/2debe1e15cc7fb0307bd0d252160b2061/adamgyenge}, description = {Chern–Simons theory on L(p,q) lens spaces and Gopakumar–Vafa duality}, doi = {http://dx.doi.org/10.1016/j.geomphys.2009.11.006}, interhash = {9b7acb688cd2fb5076019b55fa64214b}, intrahash = {debe1e15cc7fb0307bd0d252160b2061}, issn = {0393-0440}, journal = {Journal of Geometry and Physics }, keywords = {chern-simons lens space theory}, number = 3, pages = {417 - 429}, timestamp = {2016-08-17T12:44:33.000+0200}, title = {Chern–Simons theory on lens spaces and Gopakumar–Vafa duality }, url = {http://www.sciencedirect.com/science/article/pii/S0393044009001892}, volume = 60, year = 2010 }